A typical Japanese snack product with a coating that is expanded by frying is referred to the name "Onorokemame". Conventionally, "Onorokemame" is made from a formulation that contains mainly wheat flour and a large amount of expandable pregelatinized starchy flour such as pregelatinized waxy corn flour or pregelatinized glutinous rice flour that expands with heat to provide a fully expanded product. However, there was no use of the starchy flour which is less expandable but provides good savor such as mashed potato flour and corn flour, thus, a fully savory product was not obtained. In accordance with the conventional method of making "Onorokemame", the core material is coated with a layer of starchy flour that has a single degree of expandability. Accordingly, the expansion of the coating during heating is difficult to control, and hence it is difficult to provide a product that has a suitable degree of hardness. Japanese Patent Publication No. 20584/78 (corresponding to U.S. Pat. No. 4,053,650) describes a process that improves and controls the expansion of the coating simultaneously. The process involves expanding a formulation uniformly within a baking mold without using a large amount of highly expandable starchy flour. However, this process is costly because it requires the use of a special baking mold.